E-portfolio MSC indicator for a virtual learning environment

This study was conducted to identify indicators for the use of e-portfolio for a virtual learning environment in the Malaysian Skills Certification (MSC) system. The approach is through a modified Delphi technique run in three stages. The first stage is analysis of past research material and documents as guidelines in the development of questionnaire items. In the second and third stages, the developed questionnaire is distributed to experts for approval in determining e-portfolio indicators for implementation of the Malaysian Skills Certification system. The sample selected consists of 11 experts in the field of skills certification in Malaysia. Feedback from the experts was analysed using descriptive statistics (mean, median and interquartile range). The findings identify four elements (Assessment, Personal Space, Exhibition and Learning Management) and 32 indicators through a literature review. In conclusion, there are 22 indicators were identified as necessary for the implementation of the use of the e-portfolio in the Malaysian Skills Certification system

DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism

We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski and its connections with DeBruijn strings

Quantum information entropies of the eigenstates and the coherent state of the P\"oschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.Comment: Revtex4, 11 pages, 11 eps figures and a tabl

Tree-chromatic number is not equal to path-chromatic number

For a graph $G$ and a tree-decomposition $(T, \mathcal{B})$ of $G$, the chromatic number of $(T, \mathcal{B})$ is the maximum of $\chi(G[B])$, taken over all bags $B \in \mathcal{B}$. The tree-chromatic number of $G$ is the minimum chromatic number of all tree-decompositions $(T, \mathcal{B})$ of $G$. The path-chromatic number of $G$ is defined analogously. In this paper, we introduce an operation that always increases the path-chromatic number of a graph. As an easy corollary of our construction, we obtain an infinite family of graphs whose path-chromatic number and tree-chromatic number are different. This settles a question of Seymour. Our results also imply that the path-chromatic numbers of the Mycielski graphs are unbounded.Comment: 11 pages, 0 figure